The post-optimal analysis is performed among the objectives and decision variables of the obtained PO solutions to develop important relationships between them. V4 Volume of the soil pile in the area of curvature (ab) (m3) W Force acting perpendicular to the surface (bdkn) of the soil wedge (N).
Motivation
Previously, studies focused on determining the cutting force accurately during soil cutting by changing a few parameters, such as cutting depth, bulldozer speed, etc. However, to make the soil cutting operation economical and productive, the optimum input parameters must be selected.
Objectives of the Thesis
Experimental studies were also conducted to determine the accurate cutting force on a bulldozer blade. Furthermore, the post-optimal analysis (Deb and Srinivasan 2006) can be done to decipher important relationships between the objectives and decision variables.
Organization of the Report
The blade-soil interaction has been referred to in the literature as soil-blade interaction. During this interaction, enormous forces are exerted on the blade due to cohesion, adhesion and friction between the blade and the soil.
Experimental Studies
Analytical Studies
It was found that McKyes (1985) model predicted the cutting force closer to the experiment results. The models developed by Swick and Perumpral (1988) and by Qinsen and Shuren (1994) overpredicted the cutting force.
Numerical Studies
It was found that as a bulldozer blade moved forward, the horizontal component of the shear force increased. From these numerous studies, it has been found that numerical models are able to predict the shear force accurately.
Closure
In practice, the user decides on these input parameters based on experience, aiming for better soil mowing. In this chapter, the soil cutting operation is modeled for a bulldozer and its blade, emphasizing that the operation is economical and productive.
Bi-Objective Optimization Formulation
Details of Formulation
The details of both force models can be found in Appendix A, which determines the cutting force when a blade is fully loaded with soil. This objective function means that a larger volume of soil can be cut by a blade, assuming a blade is fully loaded with soil when the cutting force is determined.
Optimization Techniques
The ǫ constraint method is also used which is capable of solving convex and non-convex multi-objective optimization problems (Haimes et al. 1971). On the one hand, the constraint method converts the two-objective optimization problem into a single-objective optimization problem by considering another objective as a constraint.
Results and Discussion
- Statistical Performance Analysis of EMO Technique
- Obtained Non-Dominated Solutions
- Post-Optimal Analysis
- Guidelines for Practitioners
The relationships between the cutting force and the blade width values of the approximate PO solutions are shown in fig. In both figures, the solutions develop at the lower limit of the cutting angle. At the transition points 'w' and 'w1', the solutions develop at the upper limits of the blade height and depth of cut.
Modified Bi-Objective Optimization Formulation
Details of Formulation
The first constraint is developed for the residual power of the bulldozer engine which is given as. PR = 0.85Pbull−F ×v The second constraint is designed to prevent blade failure during the soil cutting operation. The third constraint is developed such that the production rate must be greater than TH.
Optimization Techniques
Results and Discussion
- Statistical Performance Analysis of EMO techniques . 34
- Post-Optimal Analysis
- Guidelines for Practitioners
Multi-Objective Optimization Formulation
Optimization Techniques
For the solution of the multi-objective optimization problem, five EMO techniques and the ǫ−constraint method are used. The ǫ−constraint method is used in which the objectives onN and T are converted into the constraints.
Results and Discussion
- Statistical Performance Analysis of EMO techniques . 49
- Post-Optimal Analysis
- Guidelines for Practitioners
Since different colors are used for the symbols, three groups of the approximate PO solutions can be distinguished. Again, a marginal difference in P values can be seen among the solutions obtained from both techniques. However, a solution with lowest P from the group of extension solutions can be chosen since the intervals for T and N are small.
Experimental Validation of Solutions
This is because medium and larger size blades are used at higher D and v for soil cutting, which can be seen from Fig. For example, a suitable blade can be selected from the evolved blade dimensions of the non-dominated solution. It can be seen from Fig. 3.43 that the shear strength of non-dominated solutions of model-1 shows a closer agreement with the experimental data of King et al.
Closure
The frequency with which local search is performed is another challenge where two issues can be addressed. Another issue is related to the number of solutions on which a local search can be performed. Therefore, it is necessary to design a heuristic rule to perform local search for different stages of the hybrid EMO technique.
Survey of Hybrid EMO Techniques
A weighted sum method was used and local search was used for some non-dominated solutions. Based on the gradient information, a combined objective search along repeated lines was used as a local search in (Bosman 2012). In (Ke et al. 2014), Pareto local search (PLS) was coupled with a multi-objective decomposition-based evolutionary algorithm (MOEA/D) (Zhang and Li 2007).
Approaches for Local Search Challenges
Number and Choice for Local Search
For local search, the non-dominated solutions closest to each reference line are selected. A good diverse set of non-dominated solutions can be selected to address the selection challenge. Therefore, the non-dominated solutions closest to these lines maintain good diversity between them.
Frequency of the Local Search
It is justified by the fact that (Das and Dennis 1998) approach always generates a set of structured reference points on a unit hyperplane. The reference lines drawn from these reference points are thus equally distributed in the objective space, as can be depicted from Fig. Since the starting solutions for the local search are diverse, it was expected that the improved solutions can also maintain similar diversity and help the hybrid EMO technique for faster convergence.
Hybrid EMO Technique
Results and Discussion
Test Cases
Parameters
In the proposed approach, value of pin Eq. 4.3) is set and the number of reference points is determined. Here, the motive is to determine the effect of the number of non-dominated solutions on which the local search is performed.
Convergence Plots
When comparing all versions of the hybrid EMO technique with NSGA-II, a significant improvement can be observed. In the case of q= 25, the 8 and 16 RP versions of the hybrid EMO technique converge faster than NSGA-II. It can be seen that the hybrid EMO technique converges faster than NSGA-II in all q case studies.
Closure
It was found that case 1 and case 4 of the hybrid EMO technique improved the convergence of the NSGA-II framework. Apart from the small number of RPs, the convergence was independent of the number of RPs. Validation of the obtained PO solutions with the experimental results suggests that the three-objective optimization formulation can be used in practice by the TH.
Future Work
Other forces on the ground wedge (a) Weight of the ground wedge (bcdnmk). A.12) (b) The adhesion force between the ground and the cutting edge of the blade is given as Thus, the force acting normal to the surface (bdkn) of the soil wedge is calculated as The distance is calculated as where m is the number of objectives, fmmax and fmmin are the maximum and minimum values of the mth objective function in P∗. The hypervolume indicator HV measures the hypervolume of that part of the objective space that is weakly dominated by the approximate set A.
Qinsen and Shuren (1994) Model for Wide Blade
Forces due to sheared soil sliding (abdgf) between blade and soil pile (fgde). a) The frictional force between the cut soil and the soil pile is given as b) The cohesive force between the cut soil and the soil pile is given as Forces on the fracture plane (bdkn). a) The cohesive force on the fracture plane is calculated as where C is the cohesion of the unmown soil. The vertical component of the resultant force acting on the blade is defined as an angle. A.19) Hence the resultant cutting force on the blade is calculated as
McKyes (1985) Model from Fundamental Equation of Earthmov-
The first term in the summation denotes the weight of the moving soil wedge as shown in fig. The dimensionless quantity, Nγ, is given as. A.22) Second term in the summation means cohesive force between the blade and the soil, in which Nc is given as. A.23). The magnitude of the cohesive force depends on the cohesive properties of the soil, which is quantified by the cohesion factor (C), cut depth, cut angle, friction angle between soil and wing surface, the angle that the failure plane makes with the horizontal.
NSGA-II
All EMO techniques initialize a random population and fitness is assigned to each solution of the population. All EMO techniques maintain the same population size before and after the selection and variation operators. Environmental selection is then performed to select good and above average solutions for the next generation population.
SPEA2
PAES
Then, the solutions are deleted one by one from the meshes with a larger number of non-dominant solutions to accommodate the less crowded non-dominant solutions in the archive.
SMPSO
GDE3
Here, NSGA-II environment selection is performed to select non-dominated and other good solutions for the next generation population. It should be noted that the PO solutions are constructed by copying the non-dominant solutions from the combined solutions of all 30 implementations of the EMO techniques. Then, only the non-dominated solutions are copied to make a set of PO solutions to determine the IGD value.
Inverse Generalized Distance (IGD) Indicator
Since EMO techniques are stochastic in nature, these algorithms are compared using the statistical indicators which are inverse generalized distance (IGD) indicator and hypervolume (HV) indicator.
Hypervolume (HV) Indicator
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